A class of optimal control problem for stochastic discrete-time systems with average reward reinforcement learning

In this paper, a class of optimal control problem for stochastic discrete-time systems is addressed by average reward reinforcement learning. First, the optimal control problem of the stochastic discrete-time system is transformed into a sequential decision problem for Markov decision process (MDP). It is proven that the admissible policies are gain-optimal and the optimal policy is bias-optimal with the average reward criterion, respectively. Then, sufficient conditions to almost surely (a.s.) stabilize the system are proposed. Based on the above results, an on-policy average-reward-based reinforcement learning algorithm is developed. Finally, simulation results are provided to illustrate the effectiveness of the proposed algorithm.